Triply Perfect Numbers

Many people know of perfect numbers, which in simple terms are defined as natural numbers whose proper divisors add up to the number itself (for example, the factors of 6 are 1,2, and 3, and 1+2+3 = 6). The more technical definition for a perfect number is that when the sigma function is applied to such a number, the result is double the number itself. That is, σ(n) = 2n. A triply perfect number is a number for which σ(n) = 3n.

There are six known triply perfect numbers, and it has been conjectured that there are no others. I humbly present them here, as well as the calculations used to demonstrate their triply-perfectness: